\select@language {UKenglish}
\contentsline {section}{\tocsection {}{}{Introduction}}{5}
\contentsline {part}{\tocpart {Part}{1}{Repeats}}{6}
\contentsline {section}{\tocsection {}{1}{Continuous Repeats}}{6}
\contentsline {subsection}{\tocsubsection {}{1.1}{Sequences}}{6}
\contentsline {subsection}{\tocsubsection {}{1.2}{Continuous Repeats}}{8}
\contentsline {section}{\tocsection {}{2}{Discovering Continuous Repeats}}{11}
\contentsline {subsection}{\tocsubsection {}{2.1}{Suffix Table}}{12}
\contentsline {subsection}{\tocsubsection {}{2.2}{Longest Common Prefix Table}}{13}
\contentsline {subsection}{\tocsubsection {}{2.3}{\emph {lcp-interval}}}{14}
\contentsline {subsection}{\tocsubsection {}{2.4}{Suffix Array}}{15}
\contentsline {subsection}{\tocsubsection {}{2.5}{\emph {lcp-interval} Tree}}{15}
\contentsline {subsection}{\tocsubsection {}{2.6}{Using an \emph {lcp-interval} Tree to Discover Repeats}}{16}
\contentsline {subsection}{\tocsubsection {}{2.7}{Suffix Tree}}{17}
\contentsline {subsection}{\tocsubsection {}{2.8}{Enhanced Suffix Array}}{19}
\contentsline {subsection}{\tocsubsection {}{2.9}{Child Table}}{19}
\contentsline {subsection}{\tocsubsection {}{2.10}{Burrows--Wheeler Transform Table}}{21}
\contentsline {subsection}{\tocsubsection {}{2.11}{Linearised Suffix Tree}}{22}
\contentsline {subsection}{\tocsubsection {}{2.12}{New Child Table}}{24}
\contentsline {section}{\tocsection {}{3}{Discontinuous Repeats}}{30}
\contentsline {section}{\tocsection {}{4}{Discovering Discontinuous Repeats}}{32}
\contentsline {subsection}{\tocsubsection {}{4.1}{Embedded Suffix Tree}}{36}
\contentsline {subsection}{\tocsubsection {}{4.2}{Recursively Embedded Suffix Tree}}{37}
\contentsline {part}{\tocpart {Part}{2}{Alignment}}{39}
\contentsline {section}{\tocsection {}{5}{Preliminaries}}{39}
\contentsline {subsection}{\tocsubsection {}{5.1}{Preprocessing}}{39}
\contentsline {subsection}{\tocsubsection {}{5.2}{Parallel Corpora}}{40}
\contentsline {subsection}{\tocsubsection {}{5.3}{Alignment}}{40}
\contentsline {section}{\tocsection {}{6}{Vector Space Model}}{42}
\contentsline {subsection}{\tocsubsection {}{6.1}{Vectors}}{42}
\contentsline {subsection}{\tocsubsection {}{6.2}{\emph {term-document} Matrix}}{43}
\contentsline {subsection}{\tocsubsection {}{6.3}{\emph {word\IeC {\textendash }context} Matrix}}{44}
\contentsline {subsection}{\tocsubsection {}{6.4}{Vector Space Models}}{44}
\contentsline {subsection}{\tocsubsection {}{6.5}{\emph {term frequency} $\times $ \emph {inverse document} Frequency}}{44}
\contentsline {subsection}{\tocsubsection {}{6.6}{Positive Pointwise Mutual Information}}{46}
\contentsline {subsection}{\tocsubsection {}{6.7}{Similarity}}{46}
\contentsline {section}{\tocsection {}{7}{Alignment of Discontinuous Repeats}}{47}
\contentsline {subsection}{\tocsubsection {}{7.1}{\emph {index-document} Mapping}}{47}
\contentsline {subsection}{\tocsubsection {}{7.2}{\emph {repeat-context} Matrix}}{48}
\contentsline {part}{\tocpart {Part}{3}{Implementation and Testing}}{51}
\contentsline {section}{\tocsection {}{8}{Implementation}}{51}
\contentsline {section}{\tocsection {}{9}{Testing}}{51}
\contentsline {subsection}{\tocsubsection {}{9.1}{$2$-$2$ Alignment of Discontinuous Repeats}}{51}
\contentsline {subsection}{\tocsubsection {}{9.2}{$n$-to-$m$ Alignment of Discontinuous Repeats}}{53}
\contentsline {section}{\tocsection {}{10}{Conclusion and Future Research Directions}}{55}
\contentsline {section}{\tocsection {}{}{Acknowledgments}}{56}
\contentsline {section}{\tocsection {}{}{References}}{57}
\contentsline {section}{List of Figures}{59}
\contentsline {section}{List of Tables}{60}
\contentsline {section}{\tocsection {}{}{Index}}{62}
